Math Question...

[ameriland]

An apprentice builds a machine, it takes him 15 hours longer than the master.
If both work together they are finished 5 hours earlier than when the master does it alone.
How long does it take for the master to build the machine on his own?

[Tichfield]

Not enough information to solve it.

If m=6 then a=21 and m+a=1

If m=10 then a=25 and m+a=5

etc.

[ameriland]

That's the problem I'm having... but that is all that's given...

[gen2]

It takes 15 hours for the master to build the machine on his own.

[crofter]

If the master takes T hours, then T = 15

You need to solve the equation

1/(T+15) + 1/T = 1/(T-5)

Which simplifies as

(T-15)(T+5) = 0

Hence T = 15

[ameriland]

Thanks a lot!!!

[gen2]

This is how you do it
Let m be the time taken by the master alone.

Apprentice takes (m + 15) hours to build a machine
so apprentice builds 1/(m + 15) machines in 1 hr

Master takes m hours to build a machine
so master makes 1/m machines in 1 hr

From the above we find that
Apprentics and master together will build
1/(m + 15) + 1/m machines in 1 hour


but we are told that apprentics and master together
take (m - 5) hours to build a machine
so together they make 1/(m - 5) machines per hour


Equating te ave two conclusions we get:

1/(m + 15) + 1/m = 1/(m - 5)

from now on it is just algebra.

(m + m + 15)/m(m + 15) = 1/(m - 5)

m(m + 15) = (m - 5)(2m + 15)

m^2 + 15m = 2m^2 + 5m -75

0 = m^2 - 10m - 75

0 = (m - 15)(m + 5)

so either (m - 15) = 0 implies m = 15
or (m + 5) = 0 which implies m = -5

In this situation, negative answers are meaningless

so m = 15 is the answer required.

[gen2]

Hi crofter, we seem to be in agreement on that one then.

[Postdog]

Or you post on here and let others do it....

[gen2]

Somehow my apprentics has got his keys in a muddle and should be an apprentice.

[crofter]

gen2 I must confess that I was relieved to see that we were in agreement!

[figure]

To those who answered this and other maths questions, do you all know you are doing someones homework?

[Tichfield]

I knew.

[squarebear]

I refuse to answer any questions which are obviously homework. There's a world of difference between helping someone win a quiz and doing people's schoolwork.